This paper presents a microwave absorber combining together the frequency se- lective surfaces (FSSs) and magnetic absorbing sheet for stable absorption under both TE and TM polarizations. The proposed absorber is constructed of magnetic absorbing substrate em- bedded with a periodic array of cross pattern composing a series of circular-metal-disks, and a bottom metal plane. The absorption characteristics of the magnetic absorbing substrate under both TE and TM polarizations are tuned and improved by introducing the circular-metal-disks. After optimizing the dimensions of the circular-metal-disks, the absorber with a thickness of 2.4 mm achieves a reflection coefficient less than −10 dB from 4.8 GHz to 11.0 GHz with a stable frequency response up to 30◦ for both polarizations. Meanwhile, the absorber has a wide band- width of 10.8 GHz with the incidence angle from 45◦ to 60◦ under TM polarization. The study of the current indicates that the improvement of the absorption characteristics is due to both the electric resonance and magnetic resonance.